Dynamical models of interactions between herds forage and water resources in Sahelian region. (English) Zbl 1406.92696

Summary: Optimal foraging is one of the capital topics nowadays in Sahelian region. The vast majority of feed consumed by ruminants in Sahelian region is still formed by natural pastures. Pastoral constraints are the high variability of available forage and drinking water in space and especially in time (highly seasonal, interannual variability) and the scarcity of water resources. The mobility is the main functional and opportunistic adaptation to these constraints. Our goal in this paper is to formalize two dynamical models for interactions between a herd of domesticate animals, forage resources, and water resources inside a given Sahelian area, in order to confirm, explain, and predict by mathematical models some observations about pastoralism in Sahelian region. These models in some contexts can be similar to predator-prey models as forage and water resources can be considered as preys and herd’s animals as predators. These models exhibit very rich dynamics, since it predicts abrupt changes in consumer behaviour and disponibility of forage or water resources. The dynamics exhibits a possible coexistence between herd, resources, and water with alternative peaks in their trajectories.


92D40 Ecology
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
Full Text: DOI


[1] Humanitarian Policy Group, Pastoralism, Policies and Practice in the Horn and East Africa A Review of Current Trends, (2009)
[3] Galaty, J. G.; Johnson, D. L., The World of Pastoralism: Herding Systems in Perspective, (1990), London, UK: The Guilford Press, London, UK
[4] Galaty, J. G.; Pierre, B., Herders, Warriors, and Traders: Pastoralism in Africa, (1991), Boulder, Colo, USA: Westview, Boulder, Colo, USA
[5] Department of Rural Economy and Agriculture, Policy Framework for Pastoralism in Africa: Securing, Protecting and Improving the Lives, Livelihoods and Rights of Pastoralist Communities, (2010)
[6] Carrière, M., Impact des systèmes d’élevage pastoraux sur l’environnement en Afrique et en Asie tropicale et sub-tropicale aride et sub-aride. Impact des systèmes d’élevage pastoraux sur l’environnement en Afrique et en Asie tropicale et sub-tropicale aride et sub-aride, Livestock and the Environment Finding a Balance, (1996), Scientific Environmental Monitoring Group
[7] Smith, A. B., Origins and spread of pastoralism in Africa, Nomadic Peoples, 32, 91-105, (1993)
[8] Boudet, G. K.; Audru, J.; Boudet, G.; Cesar, J., Connaissance et gestion de l’espace pastoral sahélien, Terroirs Pastoraux et Agropastoraux en Zone Tropicale. Terroirs Pastoraux et Agropastoraux en Zone Tropicale, Gestion , Aménagement et Intensification Fourragère. Etudes et Synthèses, 24, (1992)
[9] Karimata, S.
[10] Système d’Information sur le Pastoralisme au Sahel: Atlas des Évolutions des Systèmes Pastoraux au Sahel 1970–2012, (2012), FAO et CIRAD
[11] Tewa, J. J.; Djeumen, V. Y.; Bowong, S., Predator-Prey model with Holling response function of type II and SIS infectious disease, Applied Mathematical Modelling, 37, 7, 4825-4841, (2013) · Zbl 1426.92085
[12] Hsieh, Y.; Hsiao, C., Predator-prey model with disease infection in both populations, Mathematical Medicine and Biology, 25, 3, 247-266, (2008) · Zbl 1154.92040
[13] Tewa, J. J.; Bowong, S.; Oukouomi Noutchie, S. C., Mathematical analysis of a two-patch model of tuberculosis disease with staged progression, Applied Mathematical Modelling, 36, 12, 5792-5807, (2012) · Zbl 1349.92150
[14] Atangana, A.; Bildik, N., Approximate solution of tuberculosis disease population dynamics model, Abstract and Applied Analysis, 2013, (2013)
[15] Atangana, A.; Alabaraoye, E., Solving a system of fractional partial differential equations arising in the model of HIV infection of CD4 cells and attractor one-dimensional Keller- Segel equations, Advances in Difference Equations, 2013, article 94, (2013) · Zbl 1380.92026
[16] Boukal, D. S.; Křivan, V., Lyapunov functions for Lotka-Volterra predator-prey models with optimal foraging behavior, Journal of Mathematical Biology, 39, 6, 493-517, (1999) · Zbl 0976.92021
[17] Lesnoff, M.; Corniaux, C.; Hiernaux, P., Sensitivity analysis of the recovery dynamics of a cattle population following drought in the Sahel region, Ecological Modelling, 232, 28-39, (2012)
[18] Grandval, F., Pastoralism in sub-Saharan Africa: know its advantages; understand its challenges, act for its sustainability, Food Sovereignty Briefs, no. 5, (2012), Inter-Réseaux Développement Rural
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.